Crossword Genius

Bad lie mostly broadcast without forethought (2-3)

Ross

I believe the answer is:

ad-lib

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'without forethought' is the definition.
I can't judge whether this definition defines the answer.

'bad lie mostly broadcast' is the wordplay.
'mostly' means to remove the last letter (most but not all of the word).
'broadcast' indicates anagramming the letters (letters scattered or cast around).
'bad'+'lie'='badlie'
'badlie' with its last letter removed is 'badli'.
'badli' with letters rearranged gives 'AD-LIB'.

Can you help me to learn more?

(Other definitions for ad-lib that I've seen before include "Speak without preparation" , "without restraint" , "Speak off the cuff" , "spontaneous comment" , "Unprepared remark" .)

I've seen this clue in The Independent.
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